I found this today near a house site in Baltimore, dating from 1803.
It is 19+mm in diameter, two-piece construction, with backmark reading "EXTRA RICH" and "M&?" for the maker.
This must be a 19th century button.
The one aspect I see as different between the two is the length of the eagle's neck and head, otherwise very similar as you point out. Is the picture you sent a one or two-piece button?